A running shoe manufacturer believes that its supply of faulty running shoes is less than 0.03, the rate deemed acceptable. We perform a hypothesis test at a significance level of 0.05 with the null and alternative hypothesis as follows: \( H_0: p = 0.03 \) and \( H_a: p < 0.03 \).Choose the statement that best describes the significance level in the context of the hypothesis test. The significance level of 0.05 is- ○ the probability of concluding that the faulty rate is less than 0.03 when in fact the faulty rate is equal to 0.03.- ○ the z-statistic that we will use to compare the observed outcome to the null hypothesis.- ○ the rate of faulty monitors that we believe is the true rate.- ○ the probability of concluding that the faulty rate is equal to 0.03 when in fact it is less than 0.03.The option "the z-statistic that we will use to compare the observed outcome to the null hypothesis" is selected, but it is noted by the red cross as incorrect.

Suppose p is the faulty rate of supply of all running shoes.

Answered: A running shoe manufacturer believes…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The test statistic of z=2.40 is obtained when testing the claim that p>0.7. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. Find the P-value. Using a significance level of α=0.10, should we reject H0 or should we fail to reject H0?
Test the claim that the mean GPA of night students is smaller than 2.3 at the .005 significance level. The null and alternative hypothesis would be: Ho:p = 0.575 Ho:u = 2.3 Ho:4 = 2.3 Ho:p = 0.575 Ho:p = 0.575 Ho:4 = 2.3 H1:p > 0.575 H : u> 2.3 H1:4 < 2.3 H1:p < 0.575 H :p + 0.575 H1:4 # 2.3 The test is: right-tailed two-tailed left-tailed Based on a sample of 60 people, the sample mean GPA was 2.25 with a standard deviation of 0.04 The test statistic is: {to 2 decimals) The critical value is: {to 2 decimals) Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis
A medical equipment manufacturer believes that the proportion of faulty blood pressure monitors is greater than 0.11, the proportion stated by the supplier. We perform a hypothesis test at a significance level of 0.05 with the null and alternative hypothesis as follows: Ho: p = 0.11 and Ha: p < 0.11. A researcher inspects 150 items and finds 25 faulty ones. She gives a p-value of 0.01 in her analysis. Which of the following definitions is the correct interpretation of the p-value? O The probability of getting 25 or more faulty blood pressure monitors out of 150 if the true faulty rate is 0.11. The value that the z-statistic must be less than in order to reject the null hypothesis. The probability of rejecting a true null hypothesis. O The probability that the true rate of faulty items is 0.01.
Test the claim that the mean GPA of night students is smaller than 2.5 at the .05 significance level.The null and alternative hypothesis would be: H0:p=0.625H0:p=0.625H1:p>0.625H1:p>0.625 H0:p=0.625H0:p=0.625H1:p<0.625H1:p<0.625 H0:μ=2.5H0:μ=2.5H1:μ≠2.5H1:μ≠2.5 H0:p=0.625H0:p=0.625H1:p≠0.625H1:p≠0.625 H0:μ=2.5H0:μ=2.5H1:μ>2.5H1:μ>2.5 H0:μ=2.5H0:μ=2.5H1:μ<2.5H1:μ<2.5 The test is: right-tailed two-tailed left-tailed Based on a sample of 55 people, the sample mean GPA was 2.49 with a standard deviation of 0.05The test statistic is: (to 2 decimals)The critical value is: (to 2 decimals)Based on this we: Fail to reject the null hypothesis Reject the null hypothesis
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Test the claim that the proportion of people who own cats is larger than 70% at the 0.10 significance level.The null and alternative hypothesis would be: H0:p≤0.7H0:p≤0.7H1:p>0.7H1:p>0.7 H0:p=0.7H0:p=0.7H1:p≠0.7H1:p≠0.7 H0:μ≥0.7H0:μ≥0.7H1:μ<0.7H1:μ<0.7 H0:μ≤0.7H0:μ≤0.7H1:μ>0.7H1:μ>0.7 H0:μ=0.7H0:μ=0.7H1:μ≠0.7H1:μ≠0.7 H0:p≥0.7H0:p≥0.7H1:p<0.7H1:p<0.7 The test is: two-tailed left-tailed right-tailed Based on a sample of 200 people, 74% owned catsThe p-value is: (to 2 decimals)Based on this we: Reject the null hypothesis Fail to reject the null hypothesis
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Test the claim that the mean GPA of night students is smaller than 3.3 at the 0.10 significance level. The null and alternative hypothesis would be: Ho:p 0.825 Ho:p ≤ 0.825 Ho: ≤3.3 Ho: 3.3 Ho: 23.3 Ho:p> 0.825 H₁:p0.825 H₁:p> 0.825 H₁:p>3.3 H₁: 3.3 H₁: <3.3 H₁ p < 0.825 O The test is: right-tailed left-tailed two-tailed Based on a sample of 65 people, the sample mean GPA was 3.26 with a standard deviation of 0.02 The test statistic is: (to 2 decimals) The p-value is: Based on this we: O Fail to reject the null hypothesis O Reject the null hypothesis (to 2 decimals)

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